THE APPLICABILITY OF NEURAL NETWORKS IN MODELLING THE GROWTH OF SHORT FATIGUE CRACKS

This paper examines the use of a neural network to model the chaotic behaviour of the growth of short fatigue cracks which are characterized by a decreasing crack growth rate with increasing crack length. Fatigue crack growth is modelled in terms of the Hobson short fatigue crack growth law. The neural network is exclusively trained and tested on Hobson's experimental data of short fatigue cracks propagating in a 0.4% carbon steel. The empirical constants d, α and C of Hobson's growth law are determined from the neural network predictions and are found to be within the following approximate ranges 63 < d < 400 (μm), −0.27 < α < 0.08 and 1 × 10⁻⁴ < C < 509 × 10⁻⁴ with no proportional relationship observed between the constant C and the applied cyclic stress. It is shown that neural networks are a viable computational tool for modelling the chaotic behaviour of short fatigue crack growth.     

INITIATION AND GROWTH OF CRACKS IN BIAXIAL FATIGUE

Abstract— Observations of fatigue crack growth in smooth specimens under biaxial loading are reviewed, with particular reference to the Stage I to Stage II and Stage II to Stage I transitions. Further results are presented for 1% Cr-Mo-V steel and AISI 316 stainless steel at various temperatures, showing that all cracks may be classed as either Stage I or Stage II. Predictive criteria are suggested for the typè of crack obtained, and the mechanisms for elevated temperature crack initiation are discussed.     

GEL ELECTRODE IMAGING OF FATIGUE CRACKS IN MAGNESIUM ALLOYS

The gel electrode technique has been modified for the detection of fatigue cracks in magnesium alloys. Prior to fatigue loading, the surface is coated with a thin (70nm) insulating anodic film of magnesium fluoride. This film is ruptured wherever a fatigue crack subsequently forms in the magnesium alloy so that current from the gel electrode flows preferentially to the crack. This current forms an image of the crack on the gel electrode probe with a resolution of 0.05 mm. The image is repeatable, permitting the early stages of growth of small cracks to be monitored.     

FATIGUE GROWTH OF SURFACE CRACKS IN THE ELASTIC-PLASTIC REGION

Surface crack growth has been studied in centre notched and smooth panels of low carbon steel under symmetric axial elastic-plastic cyclic straining. The crack shape, followed by heat tinting, has been found to be approximately semi-circular for crack radii 0.3–5 mm. Both smooth and notched specimens have been fatigued until fracture. The smallest notches of 0.1 mm in radius and depth approximately represent defects of a critical size under present loading conditions. Crack propagation rates have been measured and plotted vs ΔJ. Both present part through-crack data and previous long through-crack data in the elastic and the elastic-plastic regions are compatible. A single dependence of dl/dN vs ΔJ is obtained.     

CLOSURE AND GROWTH OF MODE I CRACKS IN BIAXIAL FATIGUE

Abstract— —The closure behavior of mode I fatigue cracks under biaxial loading is studied with an elastic-plastic plane stress finite element model. Biaxial stresses are shown to have a significant impact on crack closure behavior at higher maximum stresses. In general, normalized crack opening stresses are highest for equibiaxial loading and lowest for pure shear loading. The differences are apparently negligible for maximum applied stresses less than about 0.4 σ₀. Experimental crack growth data are quantitatively consistent with these trends. Correlations of the experimental data with a simple Δ K _eff were successful as first-order engineering estimates. Changes in forward and reversed plastic zone sizes with biaxiality are not entirely consistent with trends in crack growth rates.     

THE GROWTH OF SMALL CORROSION FATIGUE CRACKS IN ALLOY 2024

Abstract— The corrosion fatigue crack growth characteristics of small surface and corner cracks in aluminium alloy 2024 is established. The damaging effect of salt water on the early stages of small crack growth is characterized by: (1) crack initiation at constituent particle pits, (2) intergranular microcracking for a≤100μm, and (3) transgranular small crack growth for a≥100μm. In aqueous 1% NaCl and at a constant anodic potential of −700 mV_SCE, small cracks exhibit a factor of three increase in fatigue crack growth rates compared to laboratory air. Small cracks exhibit accelerated corrosion fatigue crack growth rates at low levels of Δ K (< 1 MPa√m) below the long crack Δ K _th value. When exposed to Paris regime levels of crack tip stress intensity, small corrosion fatigue cracks exhibit growth rates similar to that observed for long cracks. Similar small and long crack growth behavior at various levels of R suggest that crack closure effects influence the corrosion fatigue crack growth rates of small cracks for a≥100 μm. Contrary to the corrosion fatigue characteristics of small cracks in high strength steels, no pronounced chemical crack length effect is observed for alloy 2024 exposed to salt water.     

子波变换在结构疲劳裂纹动态检测中的应用研究

本文利用子波分析技术,通过对带有预制裂纹的简支梁模型受迫振动时裂纹处应变响应信号进行多次子波变换,提取了淹没于强低频信号中微弱的裂纹信号分量,实验表明,这种方法能较好地获取结构裂纹处的局部应力/应变特性。     

ESTIMATING INITIATION TIMES OF SECONDARY FATIGUE CRACKS IN DAMAGE TOLERANCE ANALYSIS

Abstract— Fatigue cracking of complex structure often involves several interacting cracks developing in a sequence of crack growth, arrest and reinitiation. A "combined" method of damage tolerance analysis is presented which employs fracture mechanics concepts to calculate crack growth and fatigue data from notched coupons with the appropriate notch radius for the crack initiation phase. The notched coupon data, plotted as peak elastic notch stress vs cycles to crack initiation, are shown to be applicable even when limited yielding occurs at the notch root. For several practical reasons it is recommended to select the initial crack size, a _i, for the crack growth phase to be as large as possible, but in accord with two selection criteria. First, a _i, must be within a notch-root region wherein the elastic stress distributions near a variety of notches are virtually identical. Secondly, a _i must be small enough not to significantly influence the stress distributions for other cracks. The Combined Method is illustrated by means of an example involving fatigue crack growth along a widthwise row of holes in 305 mm wide test panels.     

FORMATION AND GROWTH OF FATIGUE CRACKS IN REINFORCING STEEL FOR CONCRETE

Abstract— –The da/d Nvs Δ Krelation for Torbar Steel is obtained by testing specimens cut from 32 mm bar. This relation is compared with available data for Unisteel 410 and with medium strength steels. Also, the pattern of fatigue cracking in Torbar is studied by inspecting bars retrieved from reinforced concrete beams which were subjected to repeated loading. It has been observed that fatigue crack locations in the bars coincided with the locations of concrete cracks traversing the bars. Tension tests on the fatigue cracked bars show that the cracks considerably reduce the ductility of the bars.     

INITIATION AND PROPAGATION OF SHORT FATIGUE CRACKS IN A WELD METAL

Abstract— Fatigue tests were performed using a purpose designed triangular shaped specimen to investigate the initiation and propagation of short fatigue cracks in a weld metal. It was observed that short fatigue cracks evolved from slip bands and were predominantly within ferrite grains. As the test progressed, the short crack density increased with minor changes in crack length. The growth of short cracks, in the early stage resulted mainly from coalescence with other existing cracks. The mechanism of short crack behaviour is discussed.     

THE GROWTH OF MICROSTRUCTURALLY SMALL FATIGUE CRACKS IN A FERRITIC-PEARLITIC STEEL

Abstract— The growth behaviour of microstructurally small fatigue cracks was investigated with smooth specimens of a ferritic-pearlitic steel, S45C. under rotating bending. The effects of microstructure, particularly the role of pearlite structure, on crack growth were evaluated based on detailed microscopic observations. In the region smaller than a certain crack length. small cracks tended to grow preferentially in the ferrite structure, and the crack growth rates decreased markedly at ferrite-pearlite boundaries when small cracks grew into the pearlite from the ferrite. The above region of crack length, i.e. the length of microstructurally small cracks, depended on stress level, increasing with decreasing stress level. The growth mechanism is also discussed in terms of the results obtained from fractogrdphy.     

PROPAGATION BEHAVIOUR OF SHORT FATIGUE CRACKS IN Q2N STEEL

Abstract— The work described in this paper characterizes short fatigue crack growth behaviour of Q2N steel having a complex microstructure and designated for pressure vessel and offshore structure applications. Short and long fatigue crack growth tests for this steel were conducted under three point bend loading conditions. It was found that, in the initial stages of growth, short cracks propagate much faster than those of long cracks when correlated with the linear elastic fracture mechanics (LEFM) parameter Δ K. A period of crack growth retardation was observed at crack lengths of approx 50 μm. The theory of the interaction between short cracks and grain boundaries fails to predict the occurrence of this deceleration minima. A new short crack deceleration mechanism is proposed based on experimental observation. Observation of the characteristic behaviour of short cracks allowed the development of a short crack growth model based on microstructural fracture mechanics analyses.     

PREDICTION OF THE LENGTH OF NON-PROPAGATING FATIGUE CRACKS

Abstract— Non-propagating cracks have been observed at notch roots by several workers. A simple linear elastic fracture mechanics model based on the Kitagawa-Takahashi diagram is presented in this paper to predict the occurrence and length of non-propagating cracks. Predicted crack lengths are compared with experimental data taken from the literature.     

PROPAGATION OF FATIGUE CRACKS UNDER POLYMODAL LOADING

Abstract— The influence of steady mode III on mode I fatigue growth behavior is investigated in four materials–a plain carbon steel, a Ni–Cr–Mo–V rotor steel, and titanium alloys, TA6V and TA5E ELI. It is shown that these loading conditions give rise to two main effects: (i) a strong reduction in propagation rate and (ii) a modification in crack path, the fatigue crack adopting a characteristic "factory-roof' aspect. In 2024 Al alloy, it is shown that the superimposition of steady mode II to cyclic mode I leads to crack bifurcation, the angle θ being a function of K _a/ K _tmax. These observations are discussed in the light of a new criterion which is introduced. This criterion is based on two main assumptions: (i) Fatigue cracking is assumed to occur only under the effect of local mode I opening. (ii) It is postulated that a fatigue crack grows in a direction where the crack propagation rate is maximum. A number of limitations of this approach, associated with crack closure phenomenon, are discussed.     

FATIGUE GROWTH OF PHYSICALLY SMALL INCLINED CRACKS

The growth of physically small, self initiated, inclined corner and through-the-width cracks is investigated in a carbon steel under tension fatigue (R= 0.05). A preliminary procedure involving crack initiation under far-field cyclic compression is used. This precracking method is adopted to minimize the effect of residual damage at the tip of the crack grown (and arrested) under cyclic compression. Thus, the subsequent tensile fatigue crack propagates through a region with no (or very small) residual stress or damage. Experiments indicate that the early growth rate of the inclined corner cracks is discontinuous with a few decelerations. During the intermittent propagation period the corner cracks only extend into the thickness (depth) of the specimen and do not propagate along the width direction. However, after reaching a certain aspect ratio, the inclined flaws grow in a steady (continuous) manner in both the thickness and width directions. Through-the-width cracks, both inclined and perpendicular to loading direction, do not show the discontinuous growth pattern typical of the inclined corner cracks, but exhibit only one minimum in the crack growth rate behaviour.     

FINITE ELEMENT ANALYSIS OF CLOSURE BEHAVIOUR OF FATIGUE CRACKS IN RESIDUAL STRESS FIELDS

An elastic-plastic finite element analysis with high order elements is performed to examine closure behaviour of fatigue. cracks in residua1 stress fieids and the numerical results are then compared with experimental results. The finite element analysis, performed under plane stress using 8-node isoparametric elements, can predict fatigue crack closure behaviour through residual stress fields very well. The crack opening and closing behaviour through a compressive residual stress field is found to be complicated and influenced by the applied load magnitude and the location of the crack tip. Three different types of crack opening behaviour, namely, normal, unsymmetric partial and symmetric partial crack opening behaviour are observed through a compressive residual stress field. The partial crack opening stress intensity factor including the partial crack opening effect is recommended for the prediction of fatigue crack growth through a compressive residual stress field.     

THE PROPAGATION OF NON-COPLANAR SEMI-ELLIPTICAL FATIGUE CRACKS

Abstract— The results of fatigue tests on specimens containing parallel offset and parallel collinear configurations of multiple non-coplanar cracks are presented. The fatigue growth of parallel collinear cracks is shown to be significantly affected by crack-tip shielding and parallel offset cracks are shown to grow almost independently before their adjacent tips overlap. Subsequent growth in the region of overlap results in coalescence which begins when the deviating crack tips come into contact below the surfaces of the specimens. Simplified predictions of the propagation of offset non-coplanar semi-elliptical cracks are also presented and their implications for the prediction of fatigue lives in structures containing offset coplanar cracks are assessed.     

COHESIVE ZONE MODELLING OF DAMAGE AT THE TIP OF CRACKS IN SLENDER BEAM STRUCTURES

The use of simple beam theory for cohesive zone modelling of the damage response at the crack tip in linear elastic isotropic double cantilever beam (DCB) specimens has been investigated. Damage resistance curves (DR-curves) relating the applied stress intensity factor to the growth of the cohesive zones for beam theory modelling has been compared with two-dimensional elasticity calculations for different material parameters and specimen dimensions. A substantial difference is observed between DR-curves for the two types of models. As expected this difference vanishes for decreasing beam heights. For large beam heights the DR-curves calculated by two-dimensional elasticity are approaching small-scale yielding DR-curves, i.e. DR-curves for an edge crack in an infinite plate. The beam height for which beam theory is applicable could be up to 10^-3 times the height for which small scale bridging DR-curves are applicable.     

SMALL FATIGUE CRACKS IN AN AUSTENITIC STAINLESS STEEL

The present study concerns nucleation and growth of small surface cracks during the low-cycle fatigue of a nitrogen-containing austenitic stainless steel. Metallographic replicas as well as longitudinal sectioning were used to record the developing crack pattern on the specimen surface. The influence of grain size and nitrogen content is considered. Small surface cracks are observed after about 10% of the fatigue life. The nucleation of cracks continues until about half of the lifetime, when the crack density saturates. This saturation phenomenon is related to the local unloading effect of growing cracks.
The mean crack length increases continuously as a power-law until specimen failure. However, small grains and a low nitrogen content amplify the effect of crack–grain boundary interactions resulting in an intermediate retardation in growth.
At high nitrogen contents, the crack growth characteristics are very much related to the slip bands formed. This results in a more simultaneous growth of cracks, a more jagged feature of the cracks introducing a higher roughness-induced crack closure effect, and, consequently, better fatigue properties.